Simplify Square Root of 139

What is the square root of 139 in its simplest radical form? To be more specific, we have created an illustration below showing what we want to calculate. Our goal is to make "A" outside the radical (√) as large as possible, and "B" inside the radical (√) as small as possible.

√139 = A√B

Unfortunately, the square root of 139 cannot be simplified. Thus, here is the answer to the square root of 139 in its simplest form:

√ 139 = √ 139

Here are two different methods we used to determine why the square root of 139 cannot be simplified.

1) To be able to simplify the square root of 139, one of the factors of 139 other than 1 must be a perfect square. The factors of 139 are 1 and 139. Since none of these factors are perfect squares, the square root of 139 cannot be simplified.

2) To be able to simplify the square root of 139, all the prime factors of 139 cannot be unique. When we did prime factorization of 139, we found that 139 equals 139. Since all the prime factors are unique, the square root of 139 cannot be simplified.

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